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CBSE has released the syllabus and assessment scheme for the 2023-24 session. Here you can see the CBSE NCERT syllabus of class 11 and 12 for Science stream - Physics, Chemistry, Math and Biology. You can also download the PDF of NCERT syllabus Class 11 and 12. The CBSE new assessment scheme will have theory, internal assessment or practical components as per the syllabus given for each subject.

- CBSE NCERT Syllabus Class 11 Physics
- CBSE NCERT Syllabus Class 12 Physics
- NCERT Syllabus for Class 11 & 12 Physics PDF Download
- CBSE NCERT Syllabus Class 11 Chemistry
- CBSE NCERT Syllabus Class 12 Chemistry
- NCERT Syllabus for Class 11 & 12 Chemistry PDF Download
- CBSE NCERT Syllabus Class 11 Math
- CBSE NCERT Syllabus Class 12 Math
- NCERT Syllabus for Class 11 & 12 Math PDF Download
- CBSE NCERT Syllabus Class 11 Biology
- CBSE NCERT Syllabus Class 12 Biology
- NCERT Syllabus for Class 11 & 12 Biology PDF Download

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The chapter and topic-wise CBSE NCERT class 11 Physics syllabus.

Chapter Name | Topics Included |
---|---|

Unit- I: Physical World and Measurement | |

Chapter–2: Units and Measurements | Need for measurement: Units of measurement; systems of units; SI units, fundamental and derived units. significant figures. Dimensions of physical quantities, dimensional analysis and its applications. |

Unit- II: Kinematics | |

Chapter–3: Motion in a Straight Line | Frame of reference, Motion in a straight line, Elementary concepts of differentiation and integration for describing motion, uniform and non- uniform motion, and instantaneous velocity, uniformly accelerated motion, velocity - time and position-time graphs. Relations for uniformly accelerated motion (graphical treatment). |

Chapter–4: Motion in a Plane | Scalar and vector quantities; position and displacement vectors, general
vectors and their notations; equality of vectors, multiplication of vectors by a
real number; addition and subtraction of vectors, Unit vector; resolution of a
vector in a plane, rectangular components, Scalar and Vector product of
vectors.
Motion in a plane, cases of uniform velocity and uniform accelerationprojectile motion, uniform circular motion. |

Unit- III: Laws of Motion | |

Chapter–5: Laws of Motion | Intuitive concept of force, Inertia, Newton's first law of motion; momentum and Newton's second law of motion; impulse; Newton's third law of motion. Law of conservation of linear momentum and its applications. Equilibrium of concurrent forces, Static and kinetic friction, laws of friction, rolling friction, lubrication. Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on a level circular road, vehicle on a banked road). |

Unit- IV: Work, Energy and Power | |

Chapter–6: Work, Energy and Power | Work done by a constant force and a variable force; kinetic energy, workenergy theorem, power. Notion of potential energy, potential energy of a spring, conservative forces: non- conservative forces, motion in a vertical circle; elastic and inelastic collisions in one and two dimensions. |

Unit- V: Motion of System of Particles and Rigid Body | |

Chapter–7: System of Particles and Rotational Motion | Centre of mass of a two-particle system, momentum conservation and Centre of mass motion. Centre of mass of a rigid body; centre of mass of a uniform rod. Moment of a force, torque, angular momentum, law of conservation of angular momentum and its applications. Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of linear and rotational motions. Moment of inertia, radius of gyration, values of moments of inertia for simple geometrical objects (no derivation). |

Unit- VI: Gravitation | |

Chapter–8: Gravitation | Kepler's laws of planetary motion, universal law of gravitation. Acceleration due to gravity and its variation with altitude and depth. Gravitational potential energy and gravitational potential, escape velocity, orbital velocity of a satellite. |

Unit- VII: Properties of Bulk Matter | |

Chapter–9: Mechanical Properties of Solids | Elasticity, Stress-strain relationship, Hooke's law, Young’s modulus, bulk modulus, shear modulus of rigidity (qualitative idea only), Poisson's ratio; elastic energy. |

Chapter–10: Mechanical Properties of Fluids | Pressure due to a fluid column; Pascal's law and its applications (hydraulic lift and hydraulic brakes), effect of gravity on fluid pressure. Viscosity, Stokes' law, terminal velocity, streamline and turbulent flow, critical velocity, Bernoulli's theorem and its simple applications. Surface energy and surface tension, angle of contact, excess of pressure across a curved surface, application of surface tension ideas to drops, bubbles and capillary rise. |

Chapter–11: Thermal Properties of Matter | Heat, temperature, thermal expansion; thermal expansion of solids, liquids and gases, anomalous expansion of water; specific heat capacity; Cp, Cv - calorimetry; change of state - latent heat capacity. Heat transfer-conduction, convection and radiation, thermal conductivity, qualitative ideas of Blackbody radiation, Wein's displacement Law, Stefan's law. |

Unit- VIII: Thermodynamics | |

Chapter–12: Thermodynamics | Thermal equilibrium and definition of temperature zeroth law of thermodynamics, heat, work and internal energy. First law of thermodynamics, Second law of thermodynamics: gaseous state of matter, change of condition of gaseous state -isothermal, adiabatic, reversible, irreversible, and cyclic processes. |

Unit- IX: Behavior of Perfect Gases and Kinetic Theory of Gases | |

Chapter–13: Kinetic Theory | Equation of state of a perfect gas, work done in compressing a gas. Kinetic theory of gases - assumptions, concept of pressure. Kinetic interpretation of temperature; rms speed of gas molecules; degrees of freedom, law of equi-partition of energy (statement only) and application to specific heat capacities of gases; concept of mean free path, Avogadro's number. |

Unit- X: Oscillations and Waves | |

Chapter–14: Oscillations | Periodic motion - time period, frequency, displacement as a function of time, periodic functions and their application. Simple harmonic motion (S.H.M) and its equations of motion; phase; oscillations of a loaded spring- restoring force and force constant; energy in S.H.M. Kinetic and potential energies; simple pendulum derivation of expression for its time period. |

Chapter–15: Waves | Wave motion: Transverse and longitudinal waves, speed of travelling wave, displacement relation for a progressive wave, principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats. |

The chapter and topic-wise CBSE NCERT class 12 Physics syllabus.

Chapter Name | Topics Included |
---|---|

Unit I: Electrostatics | |

Chapter–1: Electric Charges and Fields | Electric charges, Conservation of charge, Coulomb's law-force between twopoint charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field. Electric flux, statement of Gauss's theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside). |

Chapter–2: Electrostatic Potential and Capacitance | Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two-point charges and of electric dipole in an electrostatic field. Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarization, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor (no derivation, formulae only). |

Unit II: Current Electricity | |

Chapter–3: Current Electricity | Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current; Ohm's law, V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity, temperature dependence of resistance, Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel, Kirchhoff's rules, Wheatstone bridge. |

Unit III: Magnetic Effects of Current and Magnetism | |

Chapter–4: Moving Charges and Magnetism | Concept of magnetic field, Oersted's experiment. Biot - Savart law and its application to current carrying circular loop. Ampere's law and its applications to infinitely long straight wire. Straight solenoid (only qualitative treatment), force on a moving charge in uniform magnetic and electric fields. Force on a current-carrying conductor in a uniform magnetic field, force between two parallel current-carrying conductors-definition of ampere, torque experienced by a current loop in uniform magnetic field; Current loop as a magnetic dipole and its magnetic dipole moment, moving coil galvanometerits current sensitivity and conversion to ammeter and voltmeter. |

Chapter–5: Magnetism and Matter | Bar magnet, bar magnet as an equivalent solenoid (qualitative treatment only), magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis (qualitative treatment only), torque on a magnetic dipole (bar magnet) in a uniform magnetic field (qualitative treatment only), magnetic field lines. Magnetic properties of materials- Para-, dia- and ferro - magnetic substances with examples, Magnetization of materials, effect of temperature on magnetic properties. |

Unit IV: Electromagnetic Induction and Alternating Currents | |

Chapter–6: Electromagnetic Induction | Electromagnetic induction; Faraday's laws, induced EMF and current; Lenz's Law, Self and mutual induction. |

Chapter–7: Alternating Current | Alternating currents, peak and RMS value of alternating current/voltage; reactance and impedance; LCR series circuit (phasors only), resonance, power in AC circuits, power factor, wattless current. AC generator, Transformer. |

Unit V: Electromagnetic waves | |

Chapter–8: Electromagnetic Waves | Basic idea of displacement current, Electromagnetic waves, their characteristics, their transverse nature (qualitative idea only). Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses. |

Unit VI: Optics | |

Chapter–9: Ray Optics and Optical Instruments | Ray Optics: Reflection of light, spherical mirrors, mirror formula, refraction
of light, total internal reflection and optical fibers, refraction at spherical
surfaces, lenses, thin lens formula, lens maker’s formula, magnification,
power of a lens, combination of thin lenses in contact, refraction of light
through a prism.
Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers. |

Chapter–10: Wave Optics | Wave optics: Wave front and Huygen’s principle, reflection and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygen’s principle. Interference, Young's double slit experiment and expression for fringe width (No derivation final expression only), coherent sources and sustained interference of light, diffraction due to a single slit, width of central maxima (qualitative treatment only). |

Unit VII: Dual Nature of Radiation and Matter | |

Chapter–11: Dual Nature of Radiation and Matter | Dual nature of radiation, Photoelectric effect, Hertz and Lenard's observations; Einstein's photoelectric equation-particle nature of light. Experimental study of photoelectric effect Matter waves-wave nature of particles, de-Broglie relation. |

Unit VIII: Atoms and Nuclei | |

Chapter–12: Atoms | Alpha-particle scattering experiment; Rutherford's model of atom; Bohr model of hydrogen atom, Expression for radius of nth possible orbit, velocity and energy of electron in his orbit, of hydrogen line spectra (qualitative treatment only). |

Chapter–13: Nuclei | Composition and size of nucleus, nuclear force Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear fission, nuclear fusion. |

Unit IX: Electronic Devices | |

Chapter–14: Semiconductor Electronics: Materials, Devices and Simple Circuits | Energy bands in conductors, semiconductors and insulators (qualitative ideas only) Intrinsic and extrinsic semiconductors- p and n type, p-n junction Semiconductor diode - I-V characteristics in forward and reverse bias, application of junction diode -diode as a rectifier. |

NCERT Physics Syllabus Class 11 and 12 : Download PDF

The chapter and topic-wise CBSE NCERT class 11 Chemistry syllabus.

S No | Unit Name | Topics Included |
---|---|---|

1 | Some Basic Concepts of Chemistry | General Introduction: Importance and scope of Chemistry. Nature of matter, laws of chemical combination, Dalton's atomic theory: concept of elements, atoms and molecules. Atomic and molecular masses, mole concept and molar mass, percentage composition, empirical and molecular formula, chemical reactions, stoichiometry and calculations based on stoichiometry. |

2 | Structure of Atom | Discovery of Electron, Proton and Neutron, atomic number, isotopes and isobars. Thomson's model and its limitations. Rutherford's model and its limitations, Bohr's model and its limitations, concept of shells and subshells, dual nature of matter and light, de Broglie's relationship, Heisenberg uncertainty principle, concept of orbitals, quantum numbers, shapes of s, p and d orbitals, rules for filling electrons in orbitals - Aufbau principle, Pauli's exclusion principle and Hund's rule, electronic configuration of atoms, stability of half-filled and completely filled orbitals. |

3 | Classification of Elements and Periodicity in Properties | Significance of classification, brief history of the development of periodic table, modern periodic law and the present form of periodic table, periodic trends in properties of elements -atomic radii, ionic radii, inert gas radii, Ionization enthalpy, electron gain enthalpy, electronegativity, valency. Nomenclature of elements with atomic number greater than 100. |

4 | Chemical Bonding and Molecular Structure | Valence electrons, ionic bond, covalent bond, bond parameters, Lewis’s structure, polar character of covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR theory, concept of hybridization, involving s, p and d orbitals and shapes of some simple molecules, molecular orbital theory of homonuclear diatomic molecules (qualitative idea only), Hydrogen bond. |

6 | Chemical Thermodynamics | Concepts of System and types of systems, surroundings, work, heat, energy, extensive and intensive properties, state functions. First law of thermodynamics -internal energy and enthalpy, heat capacity and specific heat, measurement of ΔU and ΔH, Hess's law of constant heat summation, enthalpy of bond dissociation, combustion, formation, atomization, sublimation, phase transition, ionization, solution and dilution. Second law of Thermodynamics (brief introduction) Introduction of entropy as a state function, Gibb's energy change for spontaneous and non- spontaneous processes, criteria for equilibrium. Third law of thermodynamics (brief introduction). |

7 | Equilibrium | Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium - Le Chatelier's principle, ionic equilibrium- ionization of acids and bases, strong and weak electrolytes, degree of ionization, ionization of poly basic acids, acid strength, concept of pH, hydrolysis of salts (elementary idea), buffer solution, Henderson Equation, solubility product, common ion effect (with illustrative examples). |

8 | Redox Reactions | Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions, in terms of loss and gain of electrons and change in oxidation number, applications of redox reactions. |

12 | Organic Chemistry -Some Basic Principles and Techniques | General introduction, methods of purification, qualitative and quantitative analysis, classification and IUPAC nomenclature of organic compounds. Electronic displacements in a covalent bond: inductive effect, electromeric effect, resonance and hyper conjugation. Homolytic and heterolytic fission of a covalent bond: free radicals, carbocations, carbanions, electrophiles and nucleophiles, types of organic reactions. |

13 | Hydrocarbons | Classification of Hydrocarbons
Aliphatic Hydrocarbons: Alkanes - Nomenclature, isomerism, conformation (ethane only), physical properties, chemical reactions including free radical mechanism of halogenation, combustion and pyrolysis. Alkenes - Nomenclature, the structure of double bond (ethene), geometrical isomerism, physical properties, methods of preparation, chemical reactions: addition of hydrogen, halogen, water, hydrogen halides (Markovnikov's addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilic addition. Alkynes - Nomenclature, the structure of triple bond (ethyne), physical properties, methods of preparation, chemical reactions: acidic character of alkynes, addition reaction of - hydrogen, halogens, hydrogen halides and water. Aromatic Hydrocarbons: Introduction, IUPAC nomenclature, benzene: resonance, aromaticity, chemical properties: mechanism of electrophilic substitution. Nitration, sulphonation, halogenation, Friedel Craft's alkylation and acylation, directive influence of the functional group in monosubstituted benzene. Carcinogenicity and toxicity. |

The chapter and topic-wise CBSE NCERT class 12 Chemistry syllabus.

S No | Unit Name | Topics Included |
---|---|---|

2 | Solutions | Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions, Raoult's law, colligative properties - relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass, Van't Hoff factor. |

3 | Electrochemistry | Redox reactions, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells, Relation between Gibbs energy change and EMF of a cell, conductance in electrolytic solutions, specific and molar conductivity, variations of conductivity with concentration, Kohlrausch's Law, electrolysis and law of electrolysis (elementary idea), dry cell-electrolytic cells and Galvanic cells, lead accumulator, fuel cells, corrosion. |

4 | Chemical Kinetics | Rate of a reaction (Average and instantaneous), factors affecting rate of reaction: concentration, temperature, catalyst; order and molecularity of a reaction, rate law and specific rate constant, integrated rate equations and half-life (only for zero and first order reactions), concept of collision theory (elementary idea, no mathematical treatment), activation energy, Arrhenius equation. |

8 | d and f Block Elements | General introduction, electronic configuration, occurrence and characteristics of transition
metals, general trends in properties of the first-row transition metals – metallic character,
ionization enthalpy, oxidation states, ionic radii, colour, catalytic property, magnetic properties, interstitial compounds, alloy formation, preparation and properties of K2Cr2O7
and KMnO4.
Lanthanoids – Electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction and its consequences. Actinoids - Electronic configuration, oxidation states and comparison with lanthanoids. |

9 | Coordination Compounds | Coordination compounds - Introduction, ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds. Bonding, Werner's theory, VBT, and CFT; structure and stereoisomerism, the importance of coordination compounds (in qualitative analysis, extraction of metals and biological system). |

10 | Haloalkanes and Haloarenes | Haloalkanes: Nomenclature, nature of C–X bond, physical and chemical properties,
optical rotation mechanism of substitution reactions.
Haloarenes: Nature of C–X bond, substitution reactions (Directive influence of halogen in monosubstituted compounds only). Uses and environmental effects of - dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT. |

11 | Alcohols, Phenols and Ethers | Alcohols: Nomenclature, methods of preparation, physical and chemical properties (of
primary alcohols only), identification of primary, secondary and tertiary alcohols,
mechanism of dehydration, uses with special reference to methanol and ethanol.
Phenols: Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophilic substitution reactions, uses of phenols. Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses. |

12 | Aldehydes, Ketones and Carboxylic Acids | Aldehydes and Ketones: Nomenclature, nature of carbonyl group, methods of
preparation, physical and chemical properties, mechanism of nucleophilic addition,
reactivity of alpha hydrogen in aldehydes, uses.
Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses. |

13 | Amines | Amines: Nomenclature, classification, structure, methods of preparation, physical and
chemical properties, uses, identification of primary, secondary and tertiary amines.
Diazonium salts: Preparation, chemical reactions and importance in synthetic organic chemistry. |

14 | Biomolecules | Carbohydrates - Classification (aldoses and ketoses), monosaccharides (glucose and
fructose), D-L configuration oligosaccharides (sucrose, lactose, maltose), polysaccharides
(starch, cellulose, glycogen); Importance of carbohydrates.
Proteins -Elementary idea of - amino acids, peptide bond, polypeptides, proteins, structure of proteins - primary, secondary, tertiary structure and quaternary structures (qualitative idea only), denaturation of proteins; enzymes. Hormones - Elementary idea excluding structure. Vitamins - Classification and functions. Nucleic Acids: DNA and RNA. Note:The content indicated in NCERT textbooks as excluded for the year 2022-23 is not to be tested by schools. |

NCERT Chemistry Syllabus Class 11 and 12 : Download PDF

The chapter and topic-wise CBSE NCERT class 11 Math syllabus.

Chapter/ Unit Name | Topics Included |
---|---|

Unit- I: Sets and Functions | |

1. Sets | Sets and their representations, Empty set, Finite and Infinite sets, Equal sets, Subsets, Subsets of a set of real numbers especially intervals (with notations). Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement. |

2. Relations & Functions | Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the set of reals with itself (upto R x R x R).Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial representation of a function, domain, co-domain and range of a function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions. |

3. Trigonometric Functions | Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications. Deducing identities like the following: tan(x ± y) = tan x ± tan y 1 ∓ tan x tan y , cot(x ± y) = cot x cot y ∓ 1 cot y ± cot x sinα ± sinβ = 2sin 1 2 (α ± β)cos 1 2 (α ∓ β) cosα + cosβ = 2cos 1 2 (α + β)cos 1 2 (α − β) 𝑐𝑜𝑠𝛼 − 𝑐𝑜𝑠𝛽 = −2𝑠𝑖𝑛 1 2 (𝛼 + 𝛽)𝑠𝑖𝑛 1 2 (𝛼 − 𝛽) Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x and tan3x. |

Unit II: Algebra | |

1. Complex Numbers and Quadratic Equations | Need for complex numbers, especially√−1, to be motivated by inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane |

2. Linear Inequalities | Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. |

3. Permutations and Combinations | Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of Formulae for nPr and nCr and their connections, simple applications. |

4. Binomial Theorem | Historical perspective, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, simple applications. |

5. Sequence and Series | Sequence and Series. Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M. |

Unit III: Coordinate geometry | |

1. Straight Lines | Brief recall of two dimensional geometry from earlier classes. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point -slope form, slope-intercept form, two-point form, intercept form, Distance of a point from a line. |

2. Conic Sections | Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle. |

3. Introduction to Three-dimensional Geometry | Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points. |

Unit-IV : Calculus | |

1. Limits and Derivatives | Derivative introduced as rate of change both as that of distance function and geometrically. Intuitive idea of limit. Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions. Definition of derivative relate it to scope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions. |

Unit-V: Statistics and Probability | |

1. Statistics | Measures of Dispersion: Range, Mean deviation, variance and standard deviation of ungrouped/grouped data. |

2. Probability | Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with other theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events. |

The chapter and topic-wise CBSE NCERT class 12 Math syllabus.

Chapter/ Unit Name | Topics Included |
---|---|

Unit 1: Relations and Functions | |

1. Relations and Functions | Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions. |

2. Inverse Trigonometric Functions | Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. |

Unit II: Algebra | |

1. Matrices | Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Oncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries). |

2. Determinants | Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix. |

Unit-III: Calculus | |

1. Continuity and Differentiability | Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, 𝑙𝑖𝑘𝑒 sin−1 𝑥 , cos−1 𝑥 and tan−1 𝑥, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. |

2. Applications of Derivatives | Applications of derivatives: rate of change of bodies, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as reallife situations). |

3. Integrals | Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them. ∫ dx x 2 ± a 2, ∫ dx √x 2 ± a 2 , ∫ dx √a 2 − x 2 , ∫ dx ax2 + bx + c , ∫ dx √ax2+bx+c ∫ px + q ax2 + bx + c dx, ∫ px + q √ax2+bx + c dx, ∫ √a 2 ± x 2 dx, ∫ √x 2 − a 2 dx ∫√𝑎𝑥2 + 𝑏𝑥 + 𝑐 𝑑𝑥, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals. |

4. Applications of the Integrals | Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only) |

5. Differential Equations | Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: dy dx + py = q, where p and q are functions of x or constants. d𝑥 d𝑦 + px = q, where p and q are functions of y or constants. |

Unit-IV: Vectors and Three-Dimensional Geometry | |

1. Vectors | Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors. |

2. Three - dimensional Geometry | Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines. |

Unit-V: Linear Programming | |

1. Linear Programming | Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints). |

Unit-VI: Probability | |

1. Probability | Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable. |

NCERT Math Syllabus Class 11 and 12 : Download PDF

The chapter and topic-wise CBSE NCERT class 11 Biology syllabus.

Chapter/ Unit Name | Topics Included |
---|---|

Unit 1: Diversity of Living Organisms | |

Chapter-1: The Living World | Biodiversity; Need for classification; three domains of life; taxonomy and systematics; concept of species and taxonomical hierarchy; binomial nomenclature. |

Chapter-2: Biological Classification | Five kingdom classification; Salient features and classification of Monera, Protista and Fungi into major groups; Lichens, Viruses and Viroids. |

Chapter-3: Plant Kingdom | Classification of plants into major groups; Salient and distinguishing features and a few examples of Algae, Bryophyta, Pteridophyta, Gymnospermae (Topics excluded – Angiosperms, Plant Life Cycle and Alternation of Generations) |

Chapter-4: Animal Kingdom | Salient features and classification of animals, non-chordates up to phyla level and chordates up to class level (salient features and at a few examples of each category). (No live animals or specimen should be displayed.) |

Unit-II Structural Organization in Animals and Plants | |

Chapter-5: Morphology of Flowering Plants | Morphology of different parts of flowering plants: root, stem, leaf, inflorescence, flower, fruit and seed. Description of family Solanaceae. |

Chapter-6: Anatomy of Flowering Plants | Anatomy and functions of tissue systems in dicots and monocots. |

Chapter-7: Structural Organisation in Animals | Morphology, Anatomy and functions of different systems (digestive, circulatory,respiratory, nervous and reproductive) of frog. |

Unit-III Cell: Structure and Function | |

Chapter-8: Cell-The Unit of Life | Cell theory and cell as the basic unit of life, structure of prokaryotic and eukaryotic cells; Plant cell and animal cell; cell envelope; cell membrane, cell wall; cell organelles - structure and function; endomembrane system, endoplasmic reticulum, golgi bodies, lysosomes, vacuoles, mitochondria, ribosomes, plastids, microbodies; cytoskeleton, cilia, flagella, centrioles (ultrastructure and function); nucleus. |

Chapter-9: Biomolecules | Chemical constituents of living cells: biomolecules, structure and function of proteins, carbohydrates, lipids, nucleic acids; Enzyme - types, properties, enzyme action. (Topics excluded: Nature of Bond Linking Monomers in a Polymer, Dynamic State of Body Constituents – Concept of Metabolism, Metabolic Basis of Living, The Living State) |

Chapter-10: Cell Cycle and Cell Division | Cell cycle, mitosis, meiosis and their significance |

Unit-IV Plant Physiology | |

Chapter-13: Photosynthesis in Higher Plants | Photosynthesis as a means of autotrophic nutrition; site of photosynthesis, pigments involved in photosynthesis (elementary idea); photochemical and biosynthetic phases of photosynthesis; cyclic and non-cyclic photophosphorylation; chemiosmotic hypothesis; photorespiration; C3 and C4 pathways; factors affecting photosynthesis. |

Chapter-14: Respiration in Plants | Exchange of gases; cellular respiration - glycolysis, fermentation (anaerobic), TCA cycle and electron transport system (aerobic); energy relations - number of ATP molecules generated; amphibolic pathways; respiratory quotient. |

Chapter-15: Plant - Growth and Development | Seed germination; phases of plant growth and plant growth rate; conditions of growth; differentiation, dedifferentiation and redifferentiation; sequence of developmental processes in a plant cell; growth regulators - auxin, gibberellin, cytokinin, ethylene, ABA; |

Unit-V Human Physiology | |

Chapter-17: Breathing and Exchange of Gases | Respiratory organs in animals (recall only); Respiratory system in humans; mechanism of breathing and its regulation in humans - exchange of gases, transport of gases and regulation of respiration, respiratory volume; disorders related to respiration - asthma, emphysema, occupational respiratory disorders. |

Chapter-18: Body Fluids and Circulation | Composition of blood, blood groups, coagulation of blood; composition of lymph and its function; human circulatory system - Structure of human heart and blood vessels; cardiac cycle, cardiac output, ECG; double circulation; regulation of cardiac activity; disorders of circulatory system - hypertension, coronary artery disease, angina pectoris, heart failure. |

Chapter-19: Excretory Products and their Elimination | Modes of excretion - ammonotelism, ureotelism, uricotelism; human excretory system – structure and function; urine formation, osmoregulation; regulation of kidney function - renin - angiotensin, atrial natriuretic factor, ADH and diabetes insipidus; role of other organs in excretion; disorders - uremia, renal failure, renal calculi, nephritis; dialysis and artificial kidney, kidney transplant. |

Chapter-20: Locomotion and Movement | Types of movement - ciliary, flagellar, muscular; skeletal muscle, contractile proteins and muscle contraction; skeletal system and its functions; joints; disorders of muscular and skeletal systems - myasthenia gravis, tetany, muscular dystrophy, arthritis, osteoporosis, gout. |

Chapter-21: Neural Control and Coordination | Neuron and nerves; Nervous system in humans - central nervous system; peripheral nervous system and visceral nervous system; generation and conduction of nerve impulse. |

Chapter-22: Chemical Coordination and Integration | Endocrine glands and hormones; human endocrine system - hypothalamus, pituitary, pineal, thyroid, parathyroid, adrenal, pancreas, gonads; mechanism of hormone action (elementary idea); role of hormones as messengers and regulators, hypo - and hyperactivity and related disorders; dwarfism, acromegaly, cretinism, goiter, exophthalmic goitre, diabetes, Addison's disease. Note: Diseases related to all the human physiological systems to be taught in brief. |

The chapter and topic-wise CBSE NCERT class 12 Biology syllabus.

Chapter/ Unit Name | Topics Included |
---|---|

Unit-VI Reproduction | |

Chapter-2: Sexual Reproduction in Flowering Plants | Flower structure; development of male and female gametophytes; pollination - types, agencies and examples; out breeding devices; pollen-pistil interaction; double fertilization; post fertilization events - development of endosperm and embryo, development of seed and formation of fruit; special modes- apomixis, parthenocarpy, polyembryony; Significance of seed dispersal and fruit formation. |

Chapter-3: Human Reproduction | Male and female reproductive systems; microscopic anatomy of testis and ovary; gametogenesis -spermatogenesis and oogenesis; menstrual cycle; fertilisation, embryo development upto blastocyst formation, implantation; pregnancy and placenta formation (elementary idea); parturition (elementary idea); lactation (elementary idea). |

Chapter-4: Reproductive Health | Need for reproductive health and prevention of Sexually Transmitted Diseases (STDs); birth control - need and methods, contraception and medical termination of pregnancy (MTP); amniocentesis; infertility and assisted reproductive technologies - IVF, ZIFT, GIFT (elementary idea for general awareness). |

Unit-VII Genetics and Evolution | |

Chapter-5: Principles of Inheritance and Variation | Heredity and variation: Mendelian inheritance; deviations from Mendelism – incomplete dominance, co-dominance, multiple alleles and inheritance of blood groups, pleiotropy; elementary idea of polygenic inheritance; chromosome theory of inheritance; chromosomes and genes; Sex determination - in humans, birds and honey bee; linkage and crossing over; sex linked inheritance - haemophilia, colour blindness; Mendelian disorders in humans - thalassemia; chromosomal disorders in humans; Down's syndrome, Turner's and Klinefelter's syndromes. |

Chapter-6: Molecular Basis of Inheritance | Search for genetic material and DNA as genetic material; Structure of DNA and RNA; DNA packaging; DNA replication; Central Dogma; transcription, genetic code, translation; gene expression and regulation - lac operon; Genome, Human and rice genome projects; DNA fingerprinting. |

Chapter-7: Evolution | Origin of life; biological evolution and evidences for biological evolution (paleontology, comparative anatomy, embryology and molecular evidences); Darwin's contribution, modern synthetic theory of evolution; mechanism of evolution - variation (mutation and recombination) and natural selection with examples, types of natural selection; Gene flow and genetic drift; Hardy - Weinberg's principle; adaptive radiation; human evolution. |

Unit-VIII Biology and Human Welfare | |

Chapter-8: Human Health and Diseases | Pathogens; parasites causing human diseases (malaria, dengue, chikungunya, filariasis, ascariasis, typhoid, pneumonia, common cold, amoebiasis, ring worm) and their control; Basic concepts of immunology - vaccines; cancer, HIV and AIDS; Adolescence - drug and alcohol abuse. |

Chapter-10: Microbes in Human Welfare | Microbes in food processing, industrial production, sewage treatment, energy generation andmicrobes as bio-control agents and bio-fertilizers. Antibiotics; production and judicious use. |

Unit-IX Biotechnology and its Applications | |

Chapter-11: Biotechnology - Principles and Processes | Genetic Engineering (Recombinant DNA Technology). |

Chapter-12: Biotechnology and its Application | Application of biotechnology in health and agriculture: Human insulin and vaccine production, stem cell technology, gene therapy; genetically modified organisms - Bt crops; transgenic animals; biosafety issues, biopiracy and patents. |

Unit-X Ecology and Environment | |

Chapter-13: Organisms and Populations | Population interactions - mutualism, competition, predation, parasitism; population attributes - growth, birth rate and death rate, age distribution. (Topics excluded: Organism and its Environment, Major Aboitic Factors, Responses to Abioitic Factors, Adaptations) |

Chapter-14: Ecosystem | Ecosystems: Patterns, components; productivity and decomposition; energy flow; pyramids of number, biomass, energy (Topics excluded: Ecological Succession and Nutrient Cycles) |

Chapter-15: Biodiversity and its Conservation | Biodiversity-Concept, patterns, importance; loss of biodiversity; biodiversity conservation; hotspots, endangered organisms, extinction, Red Data Book, Sacred Groves, biosphere reserves, national parks, wildlife, sanctuaries and Ramsar sites. |

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